Saleh, S., Al-Mufarrij, Jawaher, Nahi Alrabeeah, Abdullah. (1402). On continuity and categorical property of interval-valued topological spaces. هنرهای کاربردی, 14(9), 385-392. doi: 10.22075/ijnaa.2023.29326.4241
S. Saleh; Jawaher Al-Mufarrij; Abdullah Abdulabbas Nahi Alrabeeah. "On continuity and categorical property of interval-valued topological spaces". هنرهای کاربردی, 14, 9, 1402, 385-392. doi: 10.22075/ijnaa.2023.29326.4241
Saleh, S., Al-Mufarrij, Jawaher, Nahi Alrabeeah, Abdullah. (1402). 'On continuity and categorical property of interval-valued topological spaces', هنرهای کاربردی, 14(9), pp. 385-392. doi: 10.22075/ijnaa.2023.29326.4241
Saleh, S., Al-Mufarrij, Jawaher, Nahi Alrabeeah, Abdullah. On continuity and categorical property of interval-valued topological spaces. هنرهای کاربردی, 1402; 14(9): 385-392. doi: 10.22075/ijnaa.2023.29326.4241

On continuity and categorical property of interval-valued topological spaces

International Journal of Nonlinear Analysis and Applications
مقاله 29، دوره 14، شماره 9، آذر 2023، صفحه 385-392    اصل مقاله (373.9 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29326.4241
نویسندگان
S. Saleh* 1، 2؛ Jawaher Al-Mufarrij3؛ Abdullah Abdulabbas Nahi Alrabeeah1
1Computer Science Department, Cihan University-Erbil, Kurdistan Region, Iraq
2Department of Mathematics, Hodeidah University-Hodeidah, Yemen
3Department of Mathematics, Women Section, King Saud University, Riyadh 12372, KSA
چکیده
An interval set (or an interval-valued set), is a special set, which is an effective tool for illustrating and describing obscure information systems and partially known problems. Recently, Kim et al.\cite{r5} defined the topological structure for interval-value sets and studied many properties of them. In this work, we discuss some characteristics and relations of continuity in interval-valued topological spaces with some necessary illustrative examples. Then we provide a categorical framework for interval-valued topological spaces $\mathcal{IV}$-$\mathcal{TOP}$. Many functors and subcategories of $\mathcal{IV}$-$\mathcal{TOP}$ are defined and studied. Furthermore, the relationships between the $\mathcal{IV}$-$\mathcal{TOP}$ and its subcategories are investigated. We show that the category $\mathcal{TOP}$ is isomorphic to the category $\mathcal{IV}$-${\mathcal{TOP}_{1}}.$ Moreover, we demonstrate that $\mathcal{TOP}$ and $\mathcal{IV}$-$\mathcal{TOP}_{1}$ are bireflective full subcategories of $\mathcal{IV}$-$\mathcal{TOP}$.
کلیدواژه‌ها
$IV$-sets؛ $IV$-topology؛ $IV$-product؛ $IV$-continuous maps؛ Category theory
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